Problem: $80$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $85$ less than $4$ times the number of away team fans. How many home team and away team fans attended the game?
Solution: Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 80}$ ${x = 4y-85}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${4y-85}$ for $x$ in the first equation. ${(4y-85)}{+ y = 80}$ Simplify and solve for $y$ $ 4y-85 + y = 80 $ $ 5y-85 = 80 $ $ 5y = 165 $ $ y = \dfrac{165}{5} $ ${y = 33}$ Now that you know ${y = 33}$ , plug it back into ${x = 4y-85}$ to find $x$ ${x = 4}{(33)}{ - 85}$ $x = 132 - 85$ ${x = 47}$ You can also plug ${y = 33}$ into ${x+y = 80}$ and get the same answer for $x$ ${x + }{(33)}{= 80}$ ${x = 47}$ There were $47$ home team fans and $33$ away team fans.